1 Best Permutations for the Dynamic Plant Layout Problem Jose M. Rodriguez †, F. Chris MacPhee ‡, David J. Bonham †, Joseph D. Horton ‡, Virendrakumar C. Bhavsar ‡ † Department of Mechanical Engineering ‡ Faculty of Computer Science University of New Brunswick Fredericton, N.B., Canada, E3B 5A3

2 Outline Introduction Problem Statement Description of the Algorithm Experimental Results Conclusions

3 Introduction Plant layout: an engineering design problem

4 Facilities Planning Process S T O Strategic Planning stages: 1.Planning (strategic level) 2.Design (tactical level) 3.Implementation (operational level). S  Objectives are determined T  Other plant layout requirements are determined O  Plant layout is selected and maintained. Plant layout objectives are determined according to: Selection of a strategy to manufacture the products (i.e., Manufacturing strategy) Definition of the products (i.e., Product design) Specification of the process plan (i.e., Process design) Definition of the production plan (i.e., Schedule design).

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6 Problem Statement The Dynamic Plant Layout Problem (DPLP) as an optimization problem [J. Balakrishnan and C. H. Cheng, “Dynamic Layout Algorithms: A State-of-the-art Survey,” International Journal of Management Science, vol. 26:4, pp , 1998.]

7 DPLP Formulation

8 Y tijl - 0,1 dependant variable for including cost of shifting facility i from location j to location l in period t A tijl - fixed cost of shifting facility i from location j to location l in period t C tijkl - cost of material flow between facility i located at j and facility k located at l in period t d jl - distance from location j to location l f tik - flow of material between facility i and facility k in period t P - number of periods n - number of facilities and locations t - a given period of the planning horizon i,k - facilities in the layout j,l - locations in the layout DPLP Formulation

9 Genetic and Tabu Search Algorithm (GATS) Overview of the GATS code The GATS search space The triangular evolutionary technique used by GATS Research questions

10 Overview of the GATS Code

11 The GATS Search Space Location of a DPLP instance cost in the GATS search space is defined by (P, CF, N), where: Population (P) refers to the number of chromosomes or layouts in the parent pool Convergence factor (CF) is the evolution threshold; a better solution must be found every CF generations or the tabu search parameters are modified Mutation (N) refers to the number of mutations to be performed between the crossover and tabu search routines

12 The Triangular Evolutionary Technique Used by GATS Synergetic Evolution (i.e., improving population quality at each generation)

13 Research Questions How many optimal layout sets are there and what are they? How many times is the layout changed during the five periods (i.e., re-layouts) and at what cost?

14 Flow/Distance matrices & shifting costs for the Rosenblatt (1986) Instance

15 GATS Early Convergence

16 GATS Final Convergence

17 GATS End of Evolution

18 An Optimal Layout Set ## Optimal --> Cost: 71187, NUM_MOVE: 4, TABU_LEN: 1, G: 138, Real G: 38 The Layout is: P= 11, cost= No.1 Period: No.2 Period: No.3 Period: No.4 Period: No.5 Period:

19 All Layout Sets Found by GATS

20 Experimental Results The GATS site: Experiments were performed on infrastructure managed by the Advanced Computational Research Laboratory at the University of New Brunswick

21 ACRL Infrastructure

22 ACRL Usage From April March 2004, GATS utilized over 11 CPU years of compute time on the ACRL chorus cluster.

23 DPLP Algorithms Genetic Algorithms CVGA - Conway, D.G. and Venkataramanan, M.A. NLGA - Balakrishnan, J. and Cheng, C.H. GADP - Balakrishnan, J., Cheng, C.H., Conway, D.G., and Lau, C.M. CCGA - Chang, M., Sugiyama, M., Ohkura, K., and Ueda, K. SymEA - Chang, M., Ohkura, K., Ueda, K., and Sugiyama, M. Simulated Annealing Algorithms SA - Baykasoglu, A. and Gindy, N.N.Z. SA, GA, DP Dynamic Programming, Genetic, and Simulated Annealing Algorithms DP-GA-SA - Erel, E., Ghosh, J.B., Simon, J.T.

24 DPLP Results Total cost of 6 department / 5 period instances

25 DPLP Results Total cost of 6 department / 10 period instances

26 DPLP Results Total cost of 15 department / 5 period instances

27 DPLP Results Total cost of 15 department / 10 period instances

28 DPLP Results Total cost of 30 department / 5 period instances

29 DPLP Results Total cost of 30 department / 10 period instances

30 Conclusions: Results GATS has been developed to solve QAP and DPLP instances. We have challenged the well- known QAPLIB, a selected DPLP dataset, and other difficult instances. Optimum or best-known permutations have been generated for over 82% of 210 available QAP and DPLP instances. Better solutions than those known to date for the DPLP have been found. Of the attempted 51 DPLP instances, 29 now have new best-known solution found by GATS.

31 Conclusions: Benefits Multiple global optima provide many benefits – equally optimal layouts by different qualitative criteria – solutions can be chosen that may have fewer layout changes, requiring fewer interruptions in the production system. Most results published in the literature include only the layout cost (no permutation). This has lead to false best known solutions and retractions. Published results should always include both costs and permutations for verification purposes.

32 Conclusions: Future Work A provisional patent regarding GATS has been filed with the United States Patent and Trademark Office. Next steps… Although the design of a factory is a planning problem, response time is as important as solution quality. The concept of ‘iterative design’ is implicit in GATS and can only be realized with a high performance computing (HPC) infrastructure.